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Class mathnetics.point2D

Extends Vector
class mathnetics.point2D
The point2D class defines a point in 2-dimensional Euclidean space via homogeneous coordinates (i.e. as a 3-vector (x,y,1)). This allows affine transformations to be applied to 2-D points via matrix multiplication.
Defined in point2D.js

Variable Summary
Number[] components
The components of the 2D point.
private int n
The "dimension" of the point; ALWAYS 2.
private Number x
The x value of the 2D point.
private Number y
The y value of the 2D point.
public static mathnetics.point2D zero
The 2-D "origin" (0,0)

Variables inherited from Vector
i, j, k

Constructor Summary
point2D (Number x, Number y)
point2D (mathnetics.point2D point)
Constructor function.

Function Summary
public mathnetics.point3D make3D()
Converts a 2D point to a 3D point with a 0 z-component.
public mathnetics.point2D map (Function func)
Maps this point to a new 2D point according to a given function.
public mathnetics.point2D rotate (Number theta)
Rotates a point through a degree theta and returns a new point.
public String toString()
Produces a string representation of the point.
public Vector toVector()
Converts point2D object back to a Vector.
public mathnetics.point2D translate (Number dx, Number dy)
Translates a point (x,y,1) to (x+dx, y+dy, 1).

Functions inherited from Vector
add, addElement, angleBetween, cross, dimension, distanceFrom, dot, elements, equalTo, get, getLength, indexOf, isAntiParallel, isParallel, isPerpendicular, linearlyDependent, linearlyIndependent, max, multiplyBy, negative, normalize, random, reflectionIn, resolute, round, snapTo, subtract, toColumnMatrix, toEach, toPoint, toRowMatrix

Variable Details

variable Number[] components

The components of the 2D point. This allows multiplication by affine transformation matrices and other useful Vector operations.

variable private int n

The "dimension" of the point; ALWAYS 2. Important that this.n != 3; gives "illusion" of 2-D vector while allowing multiplication by matrices with 3 columns for transformations

variable private Number x

The x value of the 2D point.

variable private Number y

The y value of the 2D point.

variable public static mathnetics.point2D zero

The 2-D "origin" (0,0)

Constructor Details

constructor point2D

point2D(Number x, Number y)
point2D(mathnetics.point2D point)
Constructor function. Makes a new 2D point (x,y,1).
Parameters:
components
x - the x component; if x is a point2D object, will create a duplicate of the point
y - the y component
clone
point - the point to clone

Function Details

function make3D

public mathnetics.point3D make3D()
Converts a 2D point to a 3D point with a 0 z-component.
Returns:
the 3D point

function map

public mathnetics.point2D map(Function func)
Maps this point to a new 2D point according to a given function. Overwrites the map function of the Vector class. Used internally for things like addition, multiplication, dot products, etc.
Parameters:
func - the mapping function
Returns:
the new, mapped point

function rotate

public mathnetics.point2D rotate(Number theta)
Rotates a point through a degree theta and returns a new point.
Parameters:
theta - the degree (in radians) by which to rotate the point
Returns:
a new point that is the old rotated through an angle theta

function toString

public String toString()
Produces a string representation of the point. Overwrites the toString function of the Vector class.
Returns:
the string (x,y)

function toVector

public Vector toVector()
Converts point2D object back to a Vector. Will no longer be homogeneous coordinates.
Returns:
the vector [x,y]

function translate

public mathnetics.point2D translate(Number dx, Number dy)
Translates a point (x,y,1) to (x+dx, y+dy, 1).
Parameters:
dx - the x translation
dy - the y translation
Returns:
a new point that is the old one translated